Problem: $g(t) = -3t^{2}-5t-4-3(h(t))$ $h(n) = n^{2}+2n$ $ h(g(-1)) = {?} $
Explanation: First, let's solve for the value of the inner function, $g(-1)$ . Then we'll know what to plug into the outer function. $g(-1) = -3(-1)^{2}+(-5)(-1)-4-3(h(-1))$ To solve for the value of $g$ , we need to solve for the value of $h(-1)$ $h(-1) = (-1)^{2}+(2)(-1)$ $h(-1) = -1$ That means $g(-1) = -3(-1)^{2}+(-5)(-1)-4+(-3)(-1)$ $g(-1) = 1$ Now we know that $g(-1) = 1$ . Let's solve for $h(g(-1))$ , which is $h(1)$ $h(1) = 1^{2}+(2)(1)$ $h(1) = 3$